It can be difficult to learn mathematics on your own from textbooks, and I often wish universities videotaped their mathematics courses and distributed them for free online. Fortunately, some universities do that (albeit to a very limited extent), and I hope we can compile here a list of all the mathematics courses one can view in their entirety online.

Please only post videos of entire courses; that is, a speaker giving one lecture introducing a subject to the audience should be off-limits, but a sequence of, say, 30 hour-long videos, each of which is a lecture delivered in a class would be very much on-topic.

Eleven lectures by Amritanshu Prasad on representation theory, the first two on generalities, the next five deal with representations of symmetric groups in the semisimple case, going up to the calculation of character values using Frobenius' formula. The next two deal with polynomial representations of GL(m). The last two are on the hook-length formula and Frobenius's characteristic function respectively. Assignments and notes are available on the course website for the first seven lectures.

This content is going to form the bulk of a book titled "Representation Theory: A Combinatorial Viewpoint" by the lecturer.

Might as well plug my own course on Diophantine Geometry. It's in Portuguese, so that will restrict the audience a bit, but I am having fun and it's nearly finished (last class on Nov 8th 2011). IMPA has a bunch of other videos as well, just follow the links.

If you happen to know Italian, on Massimo Gobbino's home page there are videos (tablet pc screencasts + audio) of several courses (Calculus I and II for engineers, honors calculus/analysis) and lots of high-school Math Olympiad training material.

Highly recommended: I find tablet screencasts an excellent medium, and on top of that Massimo is a great teacher.

A master course by Benoit Fresse on operads and Grothendieck-Teichmüller groups (in french), at Université Lille 1, given this semester (Winter 2012).
The course has a really nice and complete introduction to the subject. The principal reference is a preprint (in english) writed by Fresse.

It is quite an extensive list of 17 Master Classes in total. The courses are on a variety of different subjects, given by among others Maxim Kontsevich, Nicolai Reshetikhin, Nigel Hitchin, Vaughan Jones, Tom Mrowka, Gregor Masbaum, Dylan Thurston, Robert Penner and many more.